Function+Machine

Andy Jensen, Ronnie Clark || ||
 * || =The Function Machine=

=Overview= Battle the evil Function Ma'cheen to save the environment! Da Function Ma'cheen is trying to cover the earth with factories and sewage plants. Defeat it by recognizing patterns and cracking it's programming code.

The essence of algebra is recognizing patterns and generalizing them using numbers and variables. Da Function Ma'cheen iPone app will challenge the player to quickly recognize a pattern and predict the next step. Find the pattern as quickly as you can to earn points and defeat Da Function Ma'cheen. Compare your score with other players for each level.

=Instructional Objective= Players will recognize different types of patterns as quickly as they can. The patterns will increase in difficulty and complexity as the player progresses through the questions. Patterns can vary from simple color or shape patterns, to more complex numerical linear and quadratic patterns, to even more complex geometric patterns.
 * Objectives**
 * The player will accurately predict the next shape in a sequence of shapes.
 * The player will accurately predict the next value in a sequence of numbers.
 * The player will accurately describe a pattern using numbers and operation symbols.

Mathematical Reasoning** = = =Learners= This game is meant for students in grades K-12, with levels tailored to skills taught in each grade level. However, this is a fast-paced game of patterns which adults of any age may find entertaining and educational.
 * CA Math Standards: 7th Grade
 * __1.0 Students make decisions about how to approach problems__:
 * 1.1 Analyze problems by identifying relationships, distinguishing relevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
 * __2.0 Students use strategies, skills, and concepts in finding solutions__:
 * 2.4 Make and test conjectures by using both inductive and deductive reasoning.
 * 2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

=Context of Use= The game would primarily be used in a classroom, but could also be used by any student at home who has an iPhone. This game would be used as an individual activity during a center or free work period and would be used as support for struggling students or any student wanting extra practice with conjectures or pattern recognition. Each time the game is played the functions will change so that the students will not be playing the same game over again. The difficulty will increase as the player advances from one level to the next. Before the game is to be played there should be be some level of instruction on pattern recognition, especially on the higher difficulty linear and quadratic functions. After the game is completed the students will need to keep their score in hopes of beating their personal best and other scores throughout the semester. The top ten scores will be displayed on the genius list. The game is designed to be played multiple times on an iPhone or school computer. Function Machine is also designed to be played quickly and not take more than five minutes.

=Scope= The game will be a small interface, mostly used as an iPhone application and should take about 5 minutes to play. To start the game the player will need to select their skill level (easy, medium, hard or expert) Once the game begins there will be easier questions to start, that deal with shapes and color patterns and move towards more complicated number, linear, and quadratic patterns. Depending on what skill level the player chooses, the player may or may not see the more complicated linear and quadratic patterns. Hard and expert skill levels will see all the types of functions.

=Object of the Game= The goal of the game is to correctly complete as many functions as possible within the five minute period. Each player is striving to beat their own record and others in the class. The learning goal is to recognize patterns and ultimately how patterns form lines/quadratics/etc. that can be used to predict future events.

=Competing Products= One similar product is @http://www.functiongame.com Here is a Function Machine - @http://www.mathplayground.com/FunctionMachine.html And Another - @http://shodor.org/interactivate/activities/FunctionMachine/ And Another - @http://nlvm.usu.edu/en/nav/frames_asid_191_g_4_t_2.html A Variation - http://teams.lacoe.edu/documentation/classrooms/amy/algebra/5-6/activities/functionmachine/functionmachine5_6.html A very basic pattern recognition game - [] Another very basic pattern game - @http://funschool.kaboose.com/preschool/games/game_crazy_pattern_machine_the.html This is more like Master Mind - @http://pbskids.org/cyberchase/games/data/data.html This game is a guess the number in the sequence game - @http://www.funbrain.com/cracker/index.html

=Design Details=

**Design**
 * Upper left has clock
 * Upper right has score
 * Center has machine
 * Table with growing pattern on bottom
 * Table displays input and outputs as ordered pairs
 * Shake it and the multiple choice answers or keypad comes up
 * Intro screen where player chooses level (easy, medium, hard, or expert)
 * Leaderboard


 * Game Play**
 * Select Level (Easy, Medium, Hard, or Expert)
 * Numbers go into machine and outputs spit out and populate a table
 * Player shakes iPhone when ready to answer
 * Multiple choice answers for guessing outputs or keypad for guessing patterns
 * Each level of the game goes on for 5 minutes. The goal of the game is to get the highest score that you can. At the end of the level, the player can choose to replay it or move on to the next level if he/she has reached a minimum threshold of points to pass the level and unlock the next level. A player must earn at least 250 points to pass the easy level, 300 points to pass the medium level, 350 to pass the hard level, and 400 points to pass the expert level and defeat Da Function Ma'cheen.

**Specific Elements**

 * Categorization of Questions**
 * Patterns involving shapes
 * Arithmetic Sequences
 * Geometric Sequences
 * Recursive Patterns
 * Linear patterns and absolute values with all operations included (+, -, /, X)
 * Quadratic and other patterns involving exponents

Depending on the level, players will be asked to determine the output (next term) or determine what the pattern or function is. Four multiple choice answers will presented at the bottom of the screen for problems involving guessing the output. For problems involving describing the pattern, a keypad will pop up asking the player to input the pattern using only numbers and operations. If the player gives an incorrect answer in either case the correct answer will appear on the screen.

//Sample Keypad//

If players select the easy level they will be perform problems involving shapes, arithmetic, and geometric patterns. These patterns will only include one operation and no fractions will be involved. Also in the easy level players will mostly be asked to determine the output as opposed to figuring out the pattern. The medium level will include mostly the same operations, except the numbers will be mostly multi-digit and fractions may be included in arithmetic and geometric sequences. Players will more frequently be asked to describe the pattern in this level. The hard level will include linear, recursive and quadratic patterns and players will also be asked to describe the pattern. The Expert level will run the gambit of questions with higher difficulty.

//Easy// Example 1: Circle, Square, Rectangle, Circle, Square,. . . What comes next? A. Circle B. Square C. Rectangle D. Hexagon Example 2: Inputs: 1,5,8,10 Outputs: 4,8,11, ? A. 12 B. 19 C. 14 D. 13
 * Sample Questions**

//Medium// Example 1 (Geometric): Inputs: 21, 5, 63 Outputs: 63, 15, 189 Describe the pattern? Keypad pops up Example 2 (Arithmetic): Inputs: 180,29,38 Outputs: 142, -9,0 Describe the pattern? Keypad pops up Example 3 (Geometric): (1/2),(1/4),(1/8),....... What comes next? A. (1/6) B. (1/10) C. (1/16) D.(1/32)

//Hard// Example 1: Inputs 4,8,26 Outputs: 12,20,56 Keypad pops up Example 2: Inputs:10,12,4 Outputs: 100,144,16 Keypad pops up.

//Expert// Example 1: Inputs: (2/3), (5/6), (7/12) Outputs: (5/3),2,(3/2) Keypad pops up. Example 2: Inputs: 5,4,3 Outputs; 125,64,27 Keypad pops up. **Look and Sound** The overall look of the game is futuristic and cartoonish. The player is battling Da Function Ma'cheen, so there would be mechanical sounds and nature sounds, along with video game beeps and dings used to alert the player to events occurring in the game.

The scoring system is displayed in the in the upper right hand corner of the gaming screen. Each question is 10 points in value and you get an additional 10 points for consecutive answers. For example, if you answer three questions in a row you get 10 points for the first and 20 points for the second and third for a total of 50 points. You also can accumulate points by speed. The time limit is 5 minutes. For every additional 5 seconds below 5 minutes the player gets an extra 2 points. To prevent a player from running through the game without answering questions and just getting points based on time, a player must answer at least half of the questions correctly to receive additional time points. Zero points are awarded for missed questions.
 * Scoring System**

**Technical Elements**
The platform for this game is the iPhone and the software needed to create the game can be found at the following website: []. The game only needs a small screen and will utilize the motion feature (shaking) for answering questions. The file formats associated with iPhone for sound are AAC, ALAC, and MP3. The file formats preferred for graphics are gif, jpeg, and bng. The game will not have a save feature as it is only 5 minutes long.

=Motivational Issues= The challenge associated with this game is two pronged. The most important goal is to be able to guess the patterns correctly and then move onto the next level. Time is also a challenge. It is not enough to just get all the problems in a level correctly. You also have to increase your score by going quickly completing the level. Competition is a big motivational factor in the Function Machine. Playing this in a classroom players will be able to see a leaderboard, which will only include five names. This factor can be described by the [|Acquire Needs Theory], which attributes achievement as a main factor in motivation. The players will be motivated to make it on this list. Each level will have a separate leaderboard. (Modelled after [|Guitar Hero]) Using an iPhone in a classroom is motivational in itself.

=Design Process= Math teachers have taught algebraic patterns using the idea of a function machine for quite a while. The concept of a function machine is quite simple. An input (usually a number) goes into the machine, and a corresponding output comes out. These ordered pairs populate a table and provide information about the overall pattern. Pairing the function machine idea with the popularity of iPhone apps was a natural step.

The premise behind the game is that numbers go into and come out of the machine and the player guesses the pattern rule as quickly as possible. This isn't necessarily the most exciting game, though. To spice it up (and add some motivation for the player), we used:
 * Graduated point values for correct answers
 * Random inputs
 * Decreasing time to decipher patterns
 * Competition among players for top scores
 * A plot about an evil machine that is trying to take over the world

We performed internet searches to find online function games. There were quite a few, but many of them were difficult to use and they were posted on obscure websites that the average student would probably not find unless they were specifically searching for it. Creating this game for an iPhone takes advantage of the popularity of iPhone apps and the ease of use of the iPhone itself. This game has the potential to reach a significant audience.

Since we didn't have a working version of the game on an iPhone, we couldn't test the playability. However, we did share the questions and screenshots with several 6th, 7th, and 8th grade math teachers at Jean Farb Middle School. In brief interviews, they recommended another way to increase difficulty by using inputs in random order. This forces the player to find the relationship between the input and output, and not only the relationship between outputs. Easy levels could use inputs in order (1,2,3,...), and more difficult levels could use inputs in random order (3,27,-16,...). Other than that, the teachers felt that the content in the questions was appropriate for the objectives of the game. THey also thought it looked like a fun and they were interested in using it with their students if it ever gets developed further.

The biggest lesson we learned was the iterative nature of creating an egame (or any type of game, for that matter). As we came up with ideas and added different features to the game, those ideas helped us come up with others as we continually refined our game. In this way we added complexity and fun to the basic idea of a function machine.